Remark 19 The same analysis for the original Poissonized Plancherel measure \(PP(\lambda ) \propto s_{\lambda }^2 (pl_{\theta })\)  yields the Airy\(_2\)  kernel \(\mathcal {A}_2(x, y) = \int _{0}^{\infty } Ai(x+s) Ai(y+s) \mathrm {d}s\)  in the edge limit. From this perspective \(\mathcal {A}^{\pm }_{2 \rightarrow 1}\)  should be viewed as type B and C analogues of \(\mathcal {A}_2\) . This also suggests \(\mathcal {A}^{\pm }_{2 \rightarrow 1}\)  should be universal for edge behavior of symplectic and orthogonal measures — regardless of specializations, as long as the limiting action \(S\)  has a double critical point at the edge, much like \(\mathcal {A}_2\)  is universal for Schur measures with such properties. Of course this is simply the consequence of the factors \((1-w^2) (1-wz^{-1})^{-1} (1-wz)^{-1}\)  and \((1-z^2) (1-wz^{-1})^{-1} (1-wz)^{-1}\)  present in the integrals for \(K_{sp/o}\) , replacing the usual factor \((1-wz^{-1})\)  present in the case of Schur measures [1]}.

